The pressure points and rock-breaking punches Karate Kid uses don't exist, and is basically impossible for a human to archieve, no matter what training he might archieve. And human eyes and reflexes can't keep up with the lightspeed attacks that Karate Kid's does.
Actually, Karate Kid is not that much more skilled than Batman. And Batman is better at keeping his cool, and with his superior strenght and weight, Batman would triumph over Karate Kid.
They both rush each other and start to fight.
Karate kid lands blow after blow. Batman although trying his best with his vast martial arts skill just isnt fast enough to gain the upper hand on KK. His heavy suit and cape are not really as suited for hand to hand combat as KK's attire. Plus his mask also hinders his vision slightly.
KK wins.
Better clothes suited for fighting hand to hand.
Although KK suffers 2 broken hands in the process from hitting batmans armored suit. He does connect enough for the win though.